In the figure below
Question: In the figure below, $\mathrm{P}$ and $\mathrm{Q}$ are two equally intense coherent sources emitting radiation of wavelength $20 \mathrm{~m}$. The separation between $\mathrm{P}$ and $Q$ is $5 \mathrm{~m}$ and the phase of $P$ is ahead of that of $\mathrm{Q}$ by $90^{\circ} . \mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at $A, B, C$ will be in the ratio: $0: 1: 2$$4: 1: 0$$0: 1:...
Read More →A perfectly dimagnetic sphere has a small spherical
Question: A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $\overrightarrow{\mathrm{B}}$. Then the field inside the paramagnetic substance is: Zero$\overrightarrow{\mathrm{B}}$much large than $|\overrightarrow{\mathrm{B}}|$ but opposite to $\overrightarrow{\mathrm{B}}$much large than $|\overrightarrow{\mathrm{B}}|$ and parallel to $\overrightarrow{\mathrm{B}}$Correct Opt...
Read More →A double convex lens has power
Question: A double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power $1.5 \mathrm{P}$ is:$\frac{\mathrm{R}}{2}$$2 \mathrm{R}$$\frac{3 R}{2}$$\frac{\mathrm{R}}{3}$Correct Option: , 4 Solution: $\mathrm{R}_{1}=\mathrm{R}_{2}=\mathrm{R}$ Power (P) Refractive index is assume $\left(\mu_{\ell}\right)$ $\mathrm{P}=\frac{1}{\mathrm{f}}=\left(\mu_{\ell}-1\right)\left(\frac{2}{\m...
Read More →For a plane electromagnetic wave, the magnetic field at a point
Question: For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is $\overrightarrow{\mathrm{B}}(\mathrm{x}, \mathrm{t})=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right) \hat{\mathrm{k}}\right] \mathrm{T}$ The instantaneous electric field $\overrightarrow{\mathrm{E}}$ corresponding to $\overrightarrow{\mathrm{B}}$ is: (speed of light $\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}$ )$\overrightarrow{\mathrm{E}}(\mathrm{...
Read More →Solve this following
Question: A clock has a continuously moving second's hand of $0.1 \mathrm{~m}$ length. The average acceleration of the tip of the hand (in units of $\mathrm{ms}^{-2}$ ) is of the order of: $10^{-3}$$10^{-2}$$10^{-4}$$10^{-1}$Correct Option: 1 Solution: $\mathrm{R}=0.1 \mathrm{~m}$ $\omega=\frac{2 \pi}{\mathrm{T}}=\frac{2 \pi}{60}=0.105 \mathrm{rad} / \mathrm{sec}$ $a=\omega^{2} R$ $=(0.105)^{2}(0.1)$ $=0.0011$ $=1.1 \times 10^{-3}$ Average acceleration is of the order of $10^{-3}$ $\therefore$ c...
Read More →Three rods of identical cross-section and lengths
Question: Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $\mathrm{K}_{1}, \mathrm{~K}_{2}$, and $\mathrm{K}_{3}$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100^{\circ} \mathrm{C}$ and the other at $0^{\circ} \mathrm{C}$ (see figure). If the joints of the rod are at $70^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ in steady state and there is no...
Read More →An observer can see through a small hole on the side
Question: An observer can see through a small hole on the side of a jar (radius $15 \mathrm{~cm}$ ) at a point at height of $15 \mathrm{~cm}$ from the bottom (see figure). The hole is at a height of $45 \mathrm{~cm}$. When the jar is filled with a liquid up to a height of $30 \mathrm{~cm}$ the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid $\mathrm{N} / 100$, where $\mathrm{N}$ is an integer, the value of $\mathrm{N}$ is__________. Solution: $\tan ...
Read More →A person of 80kg mass is standing on the rim of a circular platform
Question: A person of $80 \mathrm{~kg}$ mass is standing on the rim of a circular platform of mass $200 \mathrm{~kg}$ rotating about its axis as 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre Solution: $\mathrm{L}_{\mathrm{i}}=\mathrm{L}_{\mathrm{f}}$ $\left(80 \mathrm{R}^{2}+\frac{200 \mathrm{R}^{2}}{2}\right) \omega=\left(0+\frac{200 \mathrm{R}^{2}}{2}...
Read More →An iron rod of volume 10^-3 m^3 and relative permeability 1000
Question: An iron rod of volume $10^{-3} \mathrm{~m}^{3}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns $/ \mathrm{cm}$. If a current of $0.5 \mathrm{~A}$ is passed through the solenoid, then the magnetic moment of the rod will be :$0.5 \times 10^{2} \mathrm{Am}^{2}$$50 \times 10^{2} \mathrm{Am}^{2}$$500 \times 10^{2} \mathrm{Am}^{2}$$5 \times 10^{2} \mathrm{Am}^{2}$Correct Option: , 4 Solution: $\mathrm{M}=\mu_{\mathrm{r}} \mathrm{NiA}$ Here $\mu_{\mathrm{r}}=$ Re...
Read More →An insect is at the bottom of a hemispherical ditch of radius
Question: An insect is at the bottom of a hemispherical ditch of radius $1 \mathrm{~m}$. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is $0.75$, then $\mathrm{h}$ is : $0.80 \mathrm{~m}$$0.60 \mathrm{~m}$$0.45 \mathrm{~m}$$0.20 \mathrm{~m}$Correct Option: 4, Solution: For balancing $m g \sin \theta=f$ $m g \sin \theta=\mu m g \cos \theta$ $\tan \theta=\mu$ $\tan \theta=\frac{3}{4}$ $h=R-R \c...
Read More →Two planets have masses
Question: Two planets have masses $\mathrm{M}$ and $16 \mathrm{M}$ and their radii are a and $2 \mathrm{a}$, respectively. The separation between the centres of the planets is $10 \mathrm{a}$. A body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :$\sqrt{\frac{\mathrm{GM}^{2}}{\mathrm{ma}}}$$\frac{3}{2} \sqrt{\frac{5 \m...
Read More →When a long glass capillary tube of radius
Question: When a long glass capillary tube of radius $0.015 \mathrm{~cm}$ is dipped in a liquid, the liquid rises to a height of $15 \mathrm{~cm}$ within it. If the contact angle between the liquid and glass to close to $0^{\circ}$, the surface tension of the liquid, in millinewton $\mathrm{m}^{-1}$, is $\left[\rho_{\text {(liquid) }}=900 \mathrm{kgm}^{-3}, \mathrm{~g}=10 \mathrm{~ms}^{-2}\right]$ (Give answer in closest integer) Solution: Capillary rise $\mathrm{h}=\frac{2 \mathrm{~S} \cos \the...
Read More →A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine
Question: A cricket ball of mass $0.15 \mathrm{~kg}$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \mathrm{~m}$ after leaving the machine. If the part pushing the ball applies a constant force $\mathrm{F}$ on the ball and moves horizontally a distance of $0.2 \mathrm{~m}$ while launching the ball, the value of $\mathrm{F}($ in $\mathrm{N})$ is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$__________. Solution: $\mathrm{W}_{\mathrm{F}}=\frac{1}{2} \mathr...
Read More →A bakelite beaker has volume capacity of 500 cc at 30 degree C.
Question: A bakelite beaker has volume capacity of $500 \mathrm{cc}$ at $30^{\circ} \mathrm{C}$. When it is partially filled with $\mathrm{V}_{\mathrm{m}}$ volume (at $30^{\circ}$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$ and $\gamma_{\text {(mercury) }}=1.5 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$, where $\gamma$ is the coefficient of volume expansion, ...
Read More →Ten charges are placed on the circumference
Question: Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+\mathrm{q})$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $\mathrm{V}$ and the electric field $\mathrm{E}$ at the centre of the circle are respectively: (Take $\mathrm{V}=0$ at infinity)$\mathrm{V}=\frac{10 \mathrm{q}}{4 \pi \in_{0} \mathrm{R}} ; \mathrm{E}=\frac{10 \mathrm{q}}{4 \pi \in_{0} \m...
Read More →A compound microscope consists of an objective
Question: A compound microscope consists of an objective lens of focal length $1 \mathrm{~cm}$ and an eye piece of focal length $5 \mathrm{~cm}$ with a separation of $10 \mathrm{~cm}$. The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{\mathrm{n}}{40} \mathrm{~cm}$. The value of $\mathrm{n}$ is Solution: Final image at $\infty$ $\Rightarrow$ obj. for eye piece at $5 \mathrm{~cm}$ $\Rightarrow$ image for objective at $5 \mathrm{~cm}$ $\frac{...
Read More →A particle of mass
Question: A particle of mass $200 \mathrm{MeV} / \mathrm{c}^{2}$ collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in $\mathrm{eV}$ ) is $\frac{\mathrm{N}}{4}$. The value of $\mathrm{N}$ is : (Given the mass of the hydrogen atom to be $1 \mathrm{GeV} / \mathrm{c}^{2}$ ) Solution: $\mathrm{mV}_{0}=\mathrm{MV}=\mathrm{p}$ $10.2=\frac{\mathrm{p}^{2}}{2 \mat...
Read More →Solve this following
Question: A particle of charge $\mathrm{q}$ and mass $\mathrm{m}$ is moving with a velocity $-v \hat{i}(v \neq 0)$ towards a large screen placed in the Y-Z plane at a distance $d$. If there is a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{k}}$, the minimum value of $v$ for which the particle will not hit the screen is: $\frac{\mathrm{qdB}_{0}}{2 \mathrm{~m}}$$\frac{q d B_{0}}{m}$$\frac{2 \mathrm{qdB}_{0}}{\mathrm{~m}}$$\frac{\mathrm{qdB}_{0}}{3 \mathrm{~m}}$Correct Op...
Read More →Two isolated conducting spheres S1 and S2 of
Question: Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 \mu C$ and $-3 \mu C$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_{1}$ and $S_{2}$ are respectively :$6 \mu \mathrm{C}$ and $3 \mu \mathrm{C}$$+4.5 \mu \mathrm{C}$ and $-4.5 \mu \mathrm{C}$$3 \mu \mathrm{C}$ and $6 \mu \mathrm{C}$$4.5 \mu \mathrm{C}$ on bothCorrect...
Read More →A beam of electrons of energy
Question: A beam of electrons of energy $E$ scatters from a target having atomic spacing of $1 A$. The first maximum intensity occurs at $\theta=60^{\circ}$. Then $\mathrm{E}$ (in $\mathrm{eV}$ ) is (Planck constant $\mathrm{h}=6.64 \times 10^{-34} \mathrm{Js}$, $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$, electron mass $\mathrm{m}=9.1 \times 10^{-31} \mathrm{~kg}$ ) Solution: $2 \mathrm{~d} \sin \theta=\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$ $2 \times 10^{-10} \times \frac{\sqrt{3}...
Read More →Prove the following
Question: Consider a gas of triatomic molecules. The molecules are assumed to the triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature $\mathrm{T}$ is :$\frac{9}{2} \mathrm{RT}$$\frac{3}{2} \mathrm{RT}$$\frac{5}{2} \mathrm{RT}$$3 \mathrm{RT}$Correct Option: , 4 Solution: $\mathrm{DOF}=3+3=6$ $\mathrm{U}=\frac{\mathrm{f}}{2} \mathrm{nRT}=3 \mathrm{RT}$...
Read More →A parallel plate capacitor has plate of length
Question: A parallel plate capacitor has plate of length ' $l$ ', width 'w' and separation of plates is 'd'. It is connected to a battery of emf V. A dielectric slab of the same thickness 'd' and of dielectric constant $\mathrm{k}=4$ is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?$l / 4$$l / 2$$l / 3$$2 l / 3$Correct Option: 3, Solution:...
Read More →Solve this following
Question: An object of mass $m$ is suspended at the end of a massless wire of length $\mathrm{L}$ and area of crosssection, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is: $\mathrm{f}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{YA}}{\mathrm{mL}}}$$f=\frac{1}{2 \pi} \sqrt{\frac{Y L}{m A}}$$f=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{mA}}{\mathrm{YL}}}$$\mathrm{f}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{mL}}{\mathrm...
Read More →A force
Question: A force $\vec{F}=(\hat{i}+2 \hat{j}+3 \hat{k}) N$ acts at a point $(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{m}$. Then the magnitude of torque about the point $(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \mathrm{m}$ will be $\sqrt{x}$ N-m. The value of $x$ is Solution: $\vec{\tau}=\left(\overrightarrow{\mathrm{r}}_{2}-\overrightarrow{\mathrm{r}}_{1}\right) \times \overrightarrow{\mathrm{F}}$ $=[(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}})-(...
Read More →Magnitude of magnetic field (in SI units) at the centre of
Question: Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side $10 \mathrm{~cm}$, 50 turns and carrying current I (Ampere) in units of $\frac{\mu_{0} I}{\pi}$ is :$250 \sqrt{3}$$5 \sqrt{3}$$500 \sqrt{3}$$50 \sqrt{3}$Correct Option: , 3 Solution: $\mathrm{B}=\frac{6 \mu_{0} \mathrm{I}}{4 \pi \mathrm{a} \cos 30^{\circ}} \times 2 \sin 30^{\circ} \times 50$ $=\frac{\mu_{0} I}{\pi} \frac{150}{\sqrt{3} a}=\frac{50 \sqrt{3}}{0.1} \frac{\mu_{0} I}{\pi}$ $=500 \sqrt{3...
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